I was living in NYC at the time and from the early reports, I think TWA 800 was brought down not by a bomb but by a shoulder fired missile that was fired from the Long Island coast. Interestingly, I heard that an El Al flight was supposed to leave at that time, but had been delayed and TWA 800 was in its slot.
However, I think the AF flight from Brazil probably was just a horrible conjunction of bad weather, a plane with problems (Airbus has already sent out messages to airlines owning this plane) and perhaps some freak malfunction.
The problem with a shoulder-fired missile bringing down TWA 800 is twofold. 1st, it was at 16,000 feet, above the service ceiling for MANPADS, second, a shoulder-fired missile would have hit an engine, rather than the fuselage. Additionally, the warhead is very small and kills with shrapnel rather than the blast.
I remember waking up with the TV on and seeing video of TWA 800 burning in the ocean. "It had to be terrorists." was my thought. It happened while they were climbing out of New York which is where I'd expect terrorists to do something like this.
The problem with a shoulder fired missile is that it would have headed into one of the engines and not necessarily downed the aircraft. The flight was almost (though not completely) out of range for a shoulder fired missile to be successful. These missiles also only burn for a second, maybe two, and just coast through the rest of their flight.
Today I'm inclined more towards the official version of events but there's always that element of doubt.
I remember hearing someone say that when they were interviewed. They broke into Larry King to talk about it moments after it happened.